Asymptotic reduction of a porous electrode model for lithium-ion batteries

TL;DR

This paper develops an asymptotic reduction of a lithium-ion battery model, simplifying it into a system of ODEs that accurately predicts battery behavior across different time scales.

Contribution

The paper introduces a novel asymptotic reduction technique that simplifies the porous electrode model into decoupled ODEs, capturing key dynamics across multiple time scales.

Findings

Model accurately predicts battery discharge curves

Reduction simplifies complex PDEs to ODEs

Excellent agreement with experiments and full simulations

Abstract

We present a porous electrode model for lithium-ion batteries using Butler--Volmer reaction kinetics. We model lithium concentration in both the solid and fluid phase along with solid and liquid electric potential. Through asymptotic reduction, we show that the electric potentials are spatially homogeneous which decouples the problem into a series of time-dependent problems. These problems can be solved on three distinguished time scales, an early time scale where capacitance effects in the electrode dominate, a mid-range time scale where a spatial concentration gradient forms in the electrolyte, and a long-time scale where each of the electrodes saturate and deplete with lithium respectively. The solid-phase concentration profiles are linear functions of time and the electrolyte potential is everywhere zero, which allows the model to be reduced to a system of two uncoupled ordinary differential equations. Analytic and numerical results are compared with full numerical simulations and experimental discharge curves demonstrating excellent agreement.